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AUTOMORPHISMS OF METABELIAN PRIME POWER ORDER GROUPS OF MAXIMAL CLASS

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 April 2008

S. FOULADI  and
R. ORFI
S. FOULADI*
Affiliation:
Faculty of Mathematics, University for Teacher Education, 599 Taleghani Avenue, Tehran 15618, Iran (email: s_fouladi@tmu.ac.ir)
R. ORFI
Affiliation:
Faculty of Mathematics, University for Teacher Education, 599 Taleghani Avenue, Tehran 15618, Iran (email: r_orfi@tmu.ac.ir)
*
✉For correspondence; e-mail: s_fouladi@tmu.ac.ir
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Abstract

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Let G be a p-group of maximal class of order pn. It is shown that the order of the group of all automorphisms of G centralizing the Frattini quotient takes the maximum value p2n−4 if and only if G is metabelian. A structure theorem is proved for the Sylow p-subgroup, Autp(G), of the automorphism group of G when G is metabelian. For p=2, Aut2(G) is the full automorphism group of G. For p=3, we prove a structure theorem for the full automorphism group of G.

Keywords

finite p-groupmaximal classmetabelian groupautomorphism group

MSC classification

Secondary: 20D45: Automorphisms 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 261 - 276
Copyright
Copyright © 2008 Australian Mathematical Society

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